Bulletin of the Institute of Combinatorics and Its Applications, 41 (2004) 71-76

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http://hdl.handle.net/1850/9696

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In 1989, George R. T. Hendry presented a table
of two-color graph Ramsey numbers R(G,H) for all pairs of graphs G and H having five vertices, with the exception of seven cases. Until now, only two of the these open cases were solved. This work eliminates another one by computing R(B_3,K_5) = 20, where B_3 = K_2 + K_3 is the book graph of order 5. In addition, we show that for these parameters there exists a unique up to isomorphism critical graph. The results are based on computer algorithms. Among the four remaining open cases in Hendry's table, the most notable is that of K_5 versus K_5, for which it is known that 43<_R(K_5,K_5)<_49.